A block rests on a floor with μ_s = 0.4. The normal force is 100 N, giving μ_s·N = 40 N. A horizontal push of 25 N is applied. What is the magnitude of the static friction force acting on the block?
A40 N — static friction always equals μ_s·N whenever an external force is applied
B25 N — static friction adjusts to exactly balance the applied force, since 25 N < 40 N and the block remains in equilibrium
C15 N — friction equals the difference between μ_s·N and the applied force
D0 N — friction only activates once the applied force exceeds the friction limit
Static friction is reactive: it takes on whatever value is needed to maintain equilibrium, up to the maximum limit μ_s·N. Here, equilibrium requires the friction force to exactly balance the 25 N push. Since 25 N < 40 N (the maximum), equilibrium is achievable and friction equals 25 N. The friction force is NOT equal to μ_s·N = 40 N — that is only the upper limit, reached only at impending motion. This is the most common misconception in friction problems: treating μ_s·N as the actual friction force rather than as its ceiling.
Question 2 Multiple Choice
You need to determine whether a block on a ramp will slide or stay stationary under a given loading. What is the correct procedure?
ASet friction = μ_s·N from the start and solve — friction is always at its maximum in equilibrium problems
BCompare the applied force to μ_k·N, the kinetic friction limit, since that governs the onset of sliding
CAssume equilibrium, apply ΣF = 0 to solve for the friction force f as an unknown, then check whether |f| ≤ μ_s·N
DThe block slides if the ramp angle exceeds the angle of the friction force
The correct approach is: (1) assume equilibrium and treat friction as an unknown, (2) apply equilibrium equations to find the required friction force f, (3) check whether |f| ≤ μ_s·N. If yes, equilibrium holds and f is the correct friction force. If no, friction cannot provide the required force and the block slides. Setting f = μ_s·N from the start (option A) is only valid when the problem explicitly states that motion is impending. Using μ_k (option B) applies only to already-sliding bodies.
Question 3 True / False
Static friction generally acts in the direction opposite to the applied external force.
TTrue
FFalse
Answer: False
Static friction opposes the *tendency of motion* — the direction the object would move if the surface were frictionless — not necessarily the direction of the applied external force. On a block resting on an incline with no other forces, gravity creates a downward-slope tendency, so friction acts up the slope (not opposite to gravity). If you also push the block hard enough up the slope, the tendency of motion reverses and friction can act down the slope. The correct rule: identify which direction the object would slide without friction, and friction acts opposite to that tendency.
Question 4 True / False
The static friction force equals μ_s times the normal force as long as the object is not moving.
TTrue
FFalse
Answer: False
μ_s·N is the *maximum* possible static friction force — the upper limit, reached only when motion is impending. For any smaller applied force, friction equals whatever value the equilibrium equations require, which is typically much less than μ_s·N. A block on a horizontal surface with no horizontal applied force has zero friction force (no tendency of motion, nothing to resist), even though μ_s·N > 0. The actual friction force is determined by the equilibrium conditions; μ_s·N is the threshold beyond which equilibrium becomes impossible.
Question 5 Short Answer
Knowing that an object is at rest is not sufficient to determine the friction force on it. What additional reasoning step is required, and why?
Think about your answer, then reveal below.
Model answer: Being at rest tells you that equilibrium holds (ΣF = 0 and ΣM = 0), but friction is a reactive force that adjusts to maintain that equilibrium. To find its value, you must apply the equilibrium equations with friction treated as an unknown force, solve for the required friction magnitude and direction, and then verify that the result does not exceed μ_s·N. The direction of friction must also be determined by identifying the tendency of motion — the direction the object would slide if the surface were frictionless — not assumed from the applied force direction.
This two-step process (solve → check) is what distinguishes friction problems from standard equilibrium problems. In a standard problem, reaction forces are uniquely determined by ΣF = 0 and ΣM = 0. In a friction problem, there are two possible outcomes — equilibrium with f < μ_s·N, or impending/actual sliding — and the equilibrium equations alone don't tell you which. The check step is not optional; it's what determines whether your assumed equilibrium is physically valid.